A Data Mining Approach for Detecting Collusion in Unproctored Online Exams
J. Langerbein, T. Massing, J. Klenke, N. Reckmann, M. Striewe,
M. Goedicke, C. Hanck
University of Duisburg-Essen; Germany
Setting
- Data from the Descriptive Statistics course at the U Duisburg-Essen, Germany
- Exams consist of arithmetical problems, programming tasks in
R, and a short essay task
- Both exams are conducted digitally with the e-assessment system JACK
- Each student receives different randomized numerical values across all tasks
- Event logs capture students’ activities, time stamps, and points during the exams for every subtask
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Comparison
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Test
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|
Year
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18/19
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20/21
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N
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109
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151
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Style
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proctocred
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unprocotored
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Total points
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60
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60
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Sub tasks
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19
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17
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Duration
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70
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70
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- The test group took the unproctored exam at home during the pandemic
- The comparison group took a proctored exam in the facilities of the university
- Data cleaning is conducted, removing students with minimal participation or achievement and students with internet problems
Aim of the Paper
Categorize students with a hierarchical clustering algorithm on event logs and strengthen the analysis with a proctored comparison group
Methodology
- The study utilized an agglomerative (bottom-up) hierarchical clustering algorithm that can be described by following equation:
\[D(s_i, s_{i'}, v_i, v_{i'}) = \frac{1}{h} \sum_{j=1}^h (w_j^P \cdot d_j^P (s_{ij}, s_{i'j}) + w_j^L \cdot d_j^L (v_{ij}, v_{i'j}))\]
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\(D(s_i, s_{i'}, v_i, v_{i'})\) the global pairwise dissimilarity
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\(d_j^P(s_{ij}, s_{i'j})\) points dissimilarity for each task \(j\)
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\(d_j^L(v_{ij}, v_{i'j})\) students event patterns dissimilarity for each task \(j\)
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\(\sum_{j=1}^h w_j^P + w_j^L =1\) weight of each attribute \(h\)
- We reduce the weights for
R-tasks, as these tasks have more noise
- Essay questions, as the comparison on that kind of task are limited
- Points achieved
- Dissimilarities in points achieved for each task \(j\)
\[d_j^P(s_{ij}, s_{i'j}) = | s_{ij} - s_{i'j} |\]
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\(s_{ij}\) denotes the points achieved by student \(i\) in the \(j\)-th subtask
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Manhatten metric
- Dissimilarities in the students event patterns (time of submission) for each task \(j\)
\[d_j^L(v_{ij}, v_{i'j}) = \sum_{m=1}^{K=70} | v_{ijm} - v_{i'jm} |\]
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\(d_j^L(v_{ij}, v_{i'j})\) students event patterns dissimilarity for each task \(j\)
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Examination is divided into \(m = 1, ... , 70\) time intervals
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\(v_{ijm}\) denotes the number of answers of student \(i\) for task \(j\) in the \(m\)-th interval
Empirical Results
- Figure 1 shows the dendrogram of the test group
- Overall a lower level of dissimilarity compared to the comparison group
- Six clusters (A-F) standing out noticeably from the rest of the cohort
- Figure 2 illustrates the individual comparison of achieved points and event logs of the student cluster with the highest similarity
- Similar time path and same points for each task
- Figure 3 compares the normalized distributions of the dissimilarity measures between the comparison and test groups
Discussion
- Three notable clusters (A, B, and E) consisting of two students each
- Collusion in larger groups are not found
- Findings the same with other linkage methods and parameter specifications as weightings
- The approach provides a basis for the examination of clusters based on comparison with a reference group